@Kreuzfeld:
Yes.
TLDR Version : (number Attacker units needed for 50% chance) = (Number of Defender units) * SQRT ( ( Average Defender Strength) / (Average Attacker Strength))
My formula is exact and easy to prove correct when you attack with only units of one type, against only units of a different type ( like inf v inf, inf v tanks, inf v ftrs, etc). I am a mathematician, I can send you the proof if you don’t trust me.
If average Defence power is 2, and average attack power is 1, then you need Sqrt(2) (1.141 number of units to win the attack 50%
I have made some calculations. If you assume you attack with only units with strength 1, and the defenders have only units of strength 2,3,4, then the number of units needed to have 50% chance of taking the terr is as follows;
1 v2 -> (sqrt(2) =) 1,41… This means that 141 infs will have less than 50%, while 142 has more than 50% against 100 infs defenders.
1v3 -> (sqrt(3) = )1.73… This means that 173 infs will have less than 50%, while 174 has more than 50% against 100 tanks defenders
1v4 -> (sqrt(4) =) 2 . So 200 infs have exactly 50% chance of winning against 100 planes.
2v4- > (sqrt(2) =) 1,41… This means that 141 art will have less than 50%, while 142 has more than 50% against 100 ftr defenders.
The main advantage of the attacking infs is that they lose less of their combatstrenght when taking losses, than defenders does. This is why they need fewer dice than the defendes.
Lets assume that the defender has the highest average strength (it the attacker has the highest, just switch it around)
The quick and dirty formula will then be :
strenghtratio = (Defenders Average Strength) / (attackers average strength)
Number of units needed for 50% to win for the attackers will then be:
#Numbers needed = SQRT(Strength Ratio) * (#Number of Defender units)
This will change depending on the “structure” of the strength, however it will not be a Huge change. The more diverse, the better the force is. A force defening force of 50% inf and 50% FTRs is better than a defending force of 100% tanks. So depending on Who I judge to have the better designed force, I add some Strength to that side when I calculate the average strength
@Kreuzfeld:
@ShadowHAwk:
Unless you can do square root calculations without a calculator ofcourse ( i surely cant )
You dont really need to, all you need is a ballpark.
If I tell you
Sqrt(1,25) = 1,12
SQRT(1,5) = 1,22
SQRT(2) = 1,41
SQRT(3) = 1,7
SQRT(4) = 2
Now, if you just remember those, you can easily guess how many units you need. You don’t actually have to calculate anything, you can just use it to get a feel for the strength. You can just go : hmmm If I put my stack next to his, can he attack? I got 60 units, how many does he have? He has 90…. opps better not do that then. Or he has 70… hmm maybe I should, or does he have too many tanks and planes among those 70?.. hmm 30 planes and tanks,… better not do that then.
If you really just want to do a short calc to get more familiar, you could count and approximate average strength and use the table from above. You will usually just have to figure out which ratio you are cloesest to among the ones in the list. The difference between 1.22 and 1.12 is rarely more than a couple of units. (unless the stacks re 50+ ofc)
So defender has 40 units, with avg strenght of 2,3 and I can attack with avg strength of 1,4. Then the ratio is about 1,5- 1.7, I should then have more than (if its 1,22) 55 units, bud do not need more than 65 units to have the minimum attack.
I use it as a tool to get a feel for the combat powers of stacks , to better evaluate my position. For me it is all about NOT having to calculate. Whenever oyu check stacks, you count number of units and number of eyes anyways. The most surprising insight this will give to many is that you need only about 1,41 to win when inf is attacking inf.
This table below is also derived on Kreuzfeld formula.
It might help visualize all he is talking about 1.41, for instance.
Lanchester’s Tables for Axis and Allies 2nd Edition
I made it on AACalc then I revised numbers by applying this formula derived from above Stack formula:
√(P2 / P1) = N1 / N2
| Avg Power
1
1.5
2
2.5
3
3.5
4
4, 2hits | 1
1.00
0.82
0.70
0.63
0.58
0.53
0.50
0.31
| 1.5
1.22
1.00
0.87
0.77
0.70
0.65
0.62
0.38
| 2
1.41
1.15
1.00
0.89
0.82
0.76
0.70
0.43
| 2.5
1.58
1.29
1.12
1.00
0.91
0.85
0.79
0.50
| 3
1.73
1.41
1.22
1.10
1.00
0.93
0.87
0.53
| 3.5
1.87
1.53
1.32
1.18
1.08
1.00
0.94
0.58
| 4
2.00
1.62
1.41
1.26
1.15
1.07
1.00
0.62
| 4, 2hits
3.33
2.64
2.30
2.00
1.87
1.73
1.62
1.00
| Avg Power
1
1.5
2
2.5
3
3.5
4
4, 2hits | 1
1:1
9:11
12:17
5:8
4:7
9:17
1:2
3:10
|
1.5
11:9
1:1
13:15
7:9
12:17
9:14
5:8
3:8
| 2
17:12
15:13
1:1
9:10
9:11
3:4
12:17
3:7
| 2.5
8:5
9:7
10:9
1:1
10:11
5:6
4:5
1:2
| 3
7:4
17:12
11:9
11:10
1:1
19:20
13:15
9:17
| 3.5
17:9
14:9
4:3
6:5
20:19
1:1
20:21
4:7
| 4
2:1
8:5
17:12
5:4
15:13
21:20
1:1
5:8
| 4, 2hits
10:3
8:3
7:3
2:1
17:9
7:4
8:5
1:1
|
|